The length of life (in years) of a personal computer is approximately normally d

Question

The length of life (in years) of a personal computer is approximately normally distributed with mean 2.9 years and variance 1.96 years.

(a) What is the probability that a randomly selected computer will last at least 2 years?

(b) What fraction of the computers will last more than 2.5 years but less than 4 years?

(c) If the manufacturer adopts a warranty policy in which only 5 percent of the computers have to be replaced, what will be the length of the warranty period?

(d) How will the length of the warranty period change in (c) if 10 percent of the computers have to be replaced?

Explanation / Answer

Since the variance is 1.96, the standard deviation is 1.96 = 1.4. We'll use the formula for the z score,

z = (x - µ)/

a) We need the z score for x = 2,

z = (2 - 2.9)/1.4 = -0.9/1.4 = -0.642857143

p(x 2) = p(z -0.642857143)

= 1 - p(z -0.642857143) = 1 - 0.2601584 = 0.7398

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